A Comparative Study of Two Allen-Cahn Models for Immiscible $N$-Phase Flows by Using a Consistent and Conservative Lattice Boltzmann Method
Year: 2024
Author: Chengjie Zhan, Xi Liu, Zhenhua Chai, Baochang Shi
Communications in Computational Physics, Vol. 36 (2024), Iss. 3 : pp. 850–876
Abstract
In this work, we conduct a detailed comparison between two second-order conservative Allen-Cahn (AC) models [Model A: Zheng et al., Phys. Rev. E 101, 0433202 (2020) and Model B: Mirjalili and Mani, J. Comput. Phys. 498, 112657 (2024)] for the immiscible $N$-phase flows. Mathematically, these two AC equations can be proved to be equivalent under some approximate conditions. However, the effects of these approximations are unclear from the theoretical point of view, and would be considered numerically. To this end, we propose a consistent and conservative lattice Boltzmann method for the AC models for $N$-phase flows, and present some numerical comparisons of accuracy and stability between these two AC models. The results show that both two AC models have good performances in accuracy, but the Model B is more stable for the realistic complex $N$-phase flows, although there is an adjustable parameter in the Model A.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2023-0228
Communications in Computational Physics, Vol. 36 (2024), Iss. 3 : pp. 850–876
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Model comparisons Allen-Cahn models $N$-phase flows lattice Boltzmann method.